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# BPSK signal set

Module by: Don Johnson. E-mail the author

Summary: Comments and exercises on BPSK

The choice of signals to represent bit values is arbitrary to some degree. Clearly, we do not want to choose signal set members to be the same; we couldn't distinguish bits if we did so. We could also have made the negative-amplitude pulse represent a 0 and the positive one a 1. This choice is indeed arbitrary and will have no effect on performance assuming the receiver knows which signal represents which bit. As in all communication systems, we design transmitter and receiver together.

A simple signal set for both wireless and wireline channels amounts to amplitude modulating a baseband signal set (more appropriate for a wireline channel) by a carrier having a frequency harmonic with the bit interval.

s 0 t=A p T tsin2πktT s 0 t A p T t 2 k t T
(1)
s 1 t=(A) p T tsin2πktT s 1 t A p T t 2 k t T
(2)

## Exercise 1

What is the value of kk in this example?

### Solution

k=4 k 4

This signal set is also known as a BPSK signal set. We'll show later that indeed both signal sets provide identical performance levels when the signal-to-noise ratios are equal.

## Exercise 2

Write a formula, in the style of the baseband signal set, for the transmitted signal as shown in the plot of the baseband signal set that emerges when we use this modulated signal.

### Solution

xt=nn-1bnA p T tnTsin2πktT x t n n -1 b n A p T t n T 2 k t T

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