Signal Sets 2.5 2000/08/14 2004/08/10 11:11:39.506 GMT-5 Don Johnson dhj@rice.edu Don Johnson dhj@rice.edu John Austin Cottrell jac3@rice.edu datarate signal set BPSK binary phase shift keying bit interval digital communication information communication Introduces binary phase shift keying. We represent a bit by associating one of two specific analog signals with the bit's value. Thus, if b n 0 , we transmit the signal s 0 t ; if b n 1 , send 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 T 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 1 t A p T t

Here, we have a baseband signal set suitable for wireline transmission. The entire bit stream b n is represented by a sequence of these signals. Mathematically, the transmitted signal has the form x t n n -1 b n A p T t n T and graphically shows what a typical transmitted signal might be.

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.

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 (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 R 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 1 T . Thus, for a 1 Mbps (megabit per second) transmission, we must have T 1 μs .