A digital radio

Though far from optimal, the receiver that you will build contains all the elements of a fully functional receiver.It provides a simple way to ask and answer what if questions. What if there is noise in the system? What if the modulation frequencies are not exactly as specified?What if there are errors in the received digits? What if the data rate is not high enough?What if there are distortion, reflections, or echoes in the transmission channel? What if the receiver is moving?

The first layer of the Software Receiver Design onion begins with a sketch of a digital radio.

An illustrative design

The first design is a brief tour of the outer layer of the onion. If some of the terminologyseems obscure or unfamiliar, rest assured that succeeding sections and chapters will revisit the words and refine theideas. The design is shown in [link] through [link] . While talking about these figures, it will become clear that some ideas are being oversimplified.Eventually, it will be necessary to come back and examine thesemore closely.

The shaded notes are reminders to return and think about these areas moredeeply later on.

In keeping with Shannon's goal of reproducing at one pointa message known at another point, suppose that it is desired to transmit a text message from one place to another.Of course, there is nothing magical about text; however, .mp3 sound files, .jpg photos, snippets of speech,raster scanned television images, or any other kind of information would do, as long as it can be appropriately digitizedinto ones and zeros.

Can every kind of message be digitized into ones and zeros?

Perhaps the simplest possible scheme would be to transmit a pulse to represent a one and to transmit nothingto represent a zero. With this scheme, however, it is hard to tell the difference betweena string of zeroes and no transmission at all. A common remedy is to send a pulse with a positive amplitude to represent a oneand a pulse of the same shape, but negative amplitude to represent a zero.In fact, if the receiver could distinguish pulses of different sizes, then it would be possible to send two bits with each symbol,for example, by associating the amplitudes Many such choices are possible. These particular values were chosen becausethey are equidistant and so noise would be no more likely to flip a 3 into a 1 than to flip a1 into a $-1$ . of $+1$ , $-1$ , $+3$ and $-3$ with the four choices 10, 01, 11, and 00.The four symbols $\pm 1$ , $\pm 3$ are called the alphabet , and the conversion from the original message (the text) into thesymbol alphabet is accomplished by the coder in the transmitter diagram [link] . The first few letters, the standard ASCII (binary) representationof these letters, and their coding into symbols are:

In this example, the symbols are clustered into groups of four, and each cluster is called a frame.Coding schemes can be designed to increase the security of a transmission, to minimize the errors, or to maximizethe rate at which data are sent. This particular scheme is not optimized in any of these senses, but it isconvenient to use in simulation studies.