Question

北美数学建模 B题 意思

<strong>PROBLEM B: Repeater Coordination </strong>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 same frequency pair (for receive and transmit); so more repeaters (and hence more users) can be accommodated in a particular area. For a circular flat area of radius 40 miles radius, determine the minimum number of repeaters necessary to accommodate 1,000 simultaneous users. Assume that the spectrum available is 145 to 148 MHz, the transmitter frequency in a repeater is either 600 kHz above or 600 kHz below the receiver frequency, and there are 54 different PL tones available. How does your solution change if there are 10,000 users? Discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas.

Answer 1

<strong>问题 b： 直放站协调</strong>甚高频无线电频谱涉及的视线的传输和接收。可以通过"留级生"拾微弱信号，放大它们，和重他们传在不同频率上克服此限制。因此，使用中继器，低功耗 （如移动站) 的用户可以进行通信与另一个的情况下直接在用户接触不可能。但是，除非他们相距足够远，或充分分离频率传输中继器可以干扰与另一个。此外地理分离、"连续色调编码静噪系统"（亚），有时绰号"私人线"(PL) 技术可以用于减轻干扰问题。这一系统将与每个中继器相关联，单独的 subaudible 音的所有用户都希望通过该直放站通信传输。直放站仅响应接收到的信号有其特定的 PL 色调。使用这个系统，附近的两个中继器可以共享相同的频率对 （用于接收和传输） ；所以更多的中继器 （并因此更多的用户） 可以安置在某一特定领域。对于半径 40 英里半径的圆形平面面积，确定中继器容纳 1000 个同时用户所需的最小数目。假设可用频谱是 145 至 148 MHz，中继器发射机频率低于接收频率，是 600 千赫以上或 600 kHz 而有 54 不同 PL 色调。您的解决方案如何改变如果有 10000 个用户？讨论这种情况可能存在缺陷的视线传播造成的山区中。