Question 1 (45 pts) Transmission Through A Bandlimited Channel A baseband 16-ary

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Question 1 (45 pts) Transmission Through A Bandlimited Channel A baseband 16-ary communication system with zero-mean AWGN is shown in the below figure where T denotes the symbol duration. The channel is an ideal LPF with bandwidth W Hz. The transmitter and receiver filters, hr(t) and hR(t), constitute a matched filter pair, ie, Hr(f)I = IHR(f)1. In the below figure the product Hr(f)11HR(f)l is shown as well Transmitter Channel Receiver wit Hd T 2T 4 T 2T 4T (a) (5 pts) Find the maximum symbol rate R,, in term of W, for which the channel will not cut the transmitted signal. (b) (15 pts) At this maximum symbol rate, does the overall system introduce ISI? Justify your answer clearly with the help of a sketch. (c) (10 pts) If W = 3 MHz, what is the maximuma bit rate, R‘, of this system? (d) (10 pts) If the bit rate has to be at least 23 Mbps, what constellation size has to be used instead of 16-ary? In other words, what would be M in the corresponding M-ary case? (e) (5 pts) Consider another LPF channel with the same W Hz bandwidth, but with non-ideal passband characteristics (i.e., channel causes spectral shaping). Given that hr(t) and hR(t) are the same as above, what operation has to be done at the receiver to remove the ill-effects caused by this channel. Discuss qualitatively

Explanation / Answer

There are 3 types of shift keying method:

1.Amplitude shift keying

2.frequency shift keying

3.phase shift keying

16-ary frequency shift keying can send four channels of data at the same time.

AWGN channel is linear addition of wieband noise

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