### Homework 2 (Due 09/07)

• 1) (10 pts) Suppose users share a 1Mbps link. Also suppose each user requires 100Kbps when transmitting, but each user transmits only 10 percent of the time.
• a) Suppose there are 40 users. Find the probability that at any given time, exactly n users are transmitting simultaneously
• b) Find the probability that there are 11 or more users transmitting simultaneously.
• 2) (36 pts) Characterizing the transmission media
• a) (8 pts) If a binary signal is sent over a 3-kHz channel whose signal-to-noise ratio (SNR) is 20dB, what is the maximum achievable data rate?
• b) (5 pts) What SNR is needed to put a T1 carrier on a 50-kHz line?
• c) (7 pts) Why is the downstream data rate limit for dial up modem 56 kbps? Assuming the bandwidth of a telephone channel is 4000 Hz.
• d) (5 pts) How much bandwidth is there in 0.1 micron of spectrum at a wavelength of 1 micron?
• e) (5 pts) Radio antennas often work best when the diameter of the antenna is equal to the wavelength of the radio wave. Reasonable antennas range from 1 cm to 5 m in diameter. What frequency range does this cover?
• f) (6 pts) According to a report, during the 1998 Tennessee-Florida game, the crowd noise measured at Neyland stadium peaked at 117dB, twice as high as the one measured at Tiger stadium during the 2000 LSU-Alabama game (111dB). In order to transmit a voice signal over this crowd at a rate of 1000bps at Neyland stadium, what kind of minimum bandwidth is required? Can you identify the type of transmission media used in this scenario?
• 3) (25 pts) On physical media
• a) (8 pts.) List 6 media types in order of increasing bandwidth (list the bandwidth as well)
• b) (4 pts.) What media is least suited for a bus geography? What media is typically used for RJ45 cable (10Base-T)?
• c) (5 pts.) What is the limiting factor in achieving high data rates on fiber? (or Why does single mode fiber have the potential to support a higher data rate than multimode fiber?)
• d) (8 pts.) Comment on the different features of satellite and fiber.
• 4) (29 pts) On communication networks
• a) (5) In a typical mobile phone system with hexagonal cells, it is forbidden to reuse a frequency band in an adjacent cell. If 840 frequencies are available, how many can be used in a given cell?
• b) (5) Calculate the maximum number of users that D-AMPS can support simultaneously within a single cell. Do the same calculation for GSM. Explain the difference.
• c) (5) D-AMPS has appreciably worse speech quality than GSM. Is this due to the requirement that D-AMPS be backward compatible with AMPS, whereas GSM had no such constraint? If not, what is the cause?
• d) (5) The 66 low-orbit satellites in the Iridium project are divided into six necklaces around the earth. At the altitude they are using, the period is 90 minutes. What is the average interval for handoffs for a stationary transmitter?
• e) (9) Suppose that A, B, and C are simultaneously transmitting 0 bits, using a CDMA system with the chip sequences of Fig. 2-45(b). What is the resulting chip sequence? Suppose a CDMA receiver gets the following chips (-1+1-3+1-1-3+1+1), which stations transmitted, and which bits did each one send?