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Transmission through AWGN Channels

Module by: Roy Ha, Mohammad Borran, Dinesh Rajan. E-mail the authors

Summary: (Blank Abstract)

Consider the problem of transmitting data through a simple additive white Gaussian noise (AWGN) channel.

Figure 1
 ()

X t X t , N t N t , and r t r t represent the transmitted, noise and received signals respectively. The received signal r t = X t + N t r t X t N t .

At the transmitter, we need to map the digital bits onto analog signals before they can be transmitted through the channel. This mapping is usually known as modulation.

Since we are considering a channel with no bandwidth restrictions, we can use rectangular pulses to represent information. On of the simplest ways of mapping the signal is to let to vary the amplitude of the pulse based on the data. Mappings based on the amplitude of the transmit pulse are called pulse amplitude modulation (PAM).

Figure 2
 ()

The data rate in fig2 is 1T 1 T bits per second. To change the data rate using PAM, we can change the symbol period TT or change the number of amplitude levels. For example, to make the data rate 2T 2 T bits per second, we can reduce the symbol period by half or we can use four amplitude levels to map the data as shown in Figure 3.

Figure 3
 ()

Another method of modulation is to use the position of the pulse to represent data. Mappings based on the position of the transmit pulse are called pulse position modulation (PPM).

Figure 4
Pulse Position Modulation (PPM)
Pulse Position Modulation (PPM) ()

At the receiver the problem is of mapping from the analog signals to the digital bits. Unsurprisingly, this mapping process is known as demodulation. Demodulation, consists of recovering the digital bit transmitted in each time slot of duration TT seconds given the received signal r t r t .

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