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Signal Sets

Module by: Don Johnson. E-mail the author

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Summary: Introduces binary phase shift keying.

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We represent a bit by associating one of two specific analog signals with the bit's value. Thus, if bn=0 b n 0 , we transmit the signal s 0 t s 0 t ; if bn=1 b n 1 , send s 1 t s 1 t . These two signals comprise the signal set for digital communication and are designed with the channel and bit stream in mind. In virtually every case, these signals have a finite duration TT common to both signals that is known as the bit interval. A commonly used example of a signal set consists of pulses that are negatives of each other.

s 0 t=A p T t s 0 t A p T t (1)
s 1 t=-A p T t s 1 t A p T t (2)

Figure 1
Figure 1 (sig26.png)

Here, we have a baseband signal set suitable for wireline transmission. The entire bit stream bn b n is represented by a sequence of these signals. Mathematically, the transmitted signal has the form

xt=∑n-1bnA p T t−nT x t n n -1 b n A p T t n T (3)
and graphically Figure 2 shows what a typical transmitted signal might be.

Figure 2: The upper plot shows how a baseband signal set for transmitting the bit sequence 0110. The lower one shows an amplitude-modulated variant suitable for wireless channels.
(a)
Figure 2(a) (sig27.png)
(b)
Figure 2(b) (sig29.png)

This way of representing a bit stream—changing the bit changes the sign of the transmitted signal—is known as binary phase shift keying and abbreviated BPSK. Here is an attempt to explain the nomenclature: The word binary is clear enough (one binary-valued quantity is transmitted during a bit interval); changing the sign of sinusoid amounts to changing — shifting — the phase by π (although we don't have a sinusoid yet); and the word "keying" reflects back to the first electrical communication system, also for digital communications: the telegraph.

The datarate RR of a digital communication system is how frequently an information bit is transmitted. In this example it equals the reciprocal of the bit interval: R=1T R 1 T . Thus, for a 1 Mbps (megabit per second) transmission, we must have T=1μs T 1 μs .

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