## Answer 6.9

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1. A 256-QAM system can convey n = log2(256) = 8 bits per symbol resulting in a symbol rate of 4 million symbols per second for a 32 Mbps data rate. For a bandpass modulation system, this requires a minimum bandwidth of 4 MHz for brick-wall filtering.
   As the actual bandwidth used is 7 MHz, this implies the use of pulse shaping with a filter having an a given by:
   (1 + a) = 7 / 4 = 1.75
   Therefore, a = 0.75.
2. The Shannon-Hartley equation gives us the required relationship between channel capacity in bits/second, the bandwidth and the signal to noise ratio as follows:
   Channel capacity C = B log2(S / N + 1) bits/second
   Therefore, C = 7 · 106 log2(10000 + 1) bits/second = 93 Mbps