Summary: Introduces a method for representing bits with an analog signal known as binary phase shift keying.
A commonly used example of a signal set consists of pulses that are negatives of each other (Figure 1).

This way of representing a bit streamchanging the bit changes
the sign of the transmitted signalis known as binary
phase shift keying and abbreviated BPSK. The name comes from concisely expressing this popular way of communicating digital information. The word "binary" is clear
enough (one binaryvalued quantity is transmitted during a bit
interval). Changing the sign of sinusoid amounts to
changingshiftingthe phase by
The datarate
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 negativeamplitude 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.
What is the value of
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 signaltonoise ratios are equal.
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.
What is the transmission bandwidth of these signal sets? We need
only consider the baseband version as the second is an
amplitudemodulated version of the first. The bandwidth is
determined by the bit sequence. If the bit sequence is
constant—always 0 or always 1—the transmitted signal
is a constant, which has zero bandwidth. The
worstcase—bandwidth consuming—bit sequence is the
alternating one shown in Figure 4. In this case, the transmitted signal is a square
wave having a period of
From our work in Fourier series, we know that this signal's
spectrum contains oddharmonics of the fundamental, which here
equals
Show that indeed the first and third harmonics contain 90%
of the transmitted power. If the receiver uses a frontend
filter of bandwidth
The harmonic distortion is 10%.
What is the 90% transmission bandwidth of the modulated signal set?
Twice the baseband bandwidth because both positive and
negative frequencies are shifted to the carrier by the
modulation:
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