Hw5_001

# Hw5_001 - ECE 5670 Digital Communications(Spring 2011...

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ECE 5670 : Digital Communications (Spring 2011) Homework 5 Due March 3 in class Instructor: Salman Avestimehr Oﬃce 325 Rhodes Hall 1. Determine the bit rate that can be transmitted through an ideal 4kHz channel if the following modulations are used: (a) binary PAM, and (b) 16-PAM. Assume that the transmitter pulse shape has a raised-cosine spectrum with a 50% roll-oﬀ (i.e., β = 0 . 5). 2. An ideal 4kHz channel (i.e., with bandwidth [-2 kHz, 2kHz]) is to be used for transmis- sion of data at a rate of 9600 bits/s. If 1 2 N 0 = 10 - 10 Watt/Hz is the spectral density of the additive, zero-mean Gaussian noise, design a PAM modulation and determine the average power that achieves a bit error probability of 10 - 6 . Use a raised-cosine transmitter pulse shape with a roll-oﬀ factor of at least 50%. 3. It is known that the capacity of a certain AWGN channel is 56 kbps (kilo bits per second). Identify which of the following statements are true (more than one may be true). (a) With an appropriate transmitter and nearest neighbor receiver, arbitrarily reli-

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Hw5_001 - ECE 5670 Digital Communications(Spring 2011...

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