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What are the definitions of signal and symbol in wireless communications, respectively? Often when I read books and papers I see things like "transmitted signal" and "transmitted symbol". Is there a difference? I tried searching online, but most results treat them as just words in English, not as concepts in wireless communications. I am new to this field and I'd appreciate any help.

For example, in the paper Beamforming Design for Large-Scale Antenna Arrays Using Deep Learning by Lin and Zhu, the words appear in the same paragraph introducing the system model:

Let s denote the transmitted symbol with normalized average symbol energy, i.e., E{|s|^2} = 1. The symbol is first multiplied by a scalar digital precoder v_{D}, and then by an Nt × 1 analog precoder v_{RF}, which is implemented using phase shifters. The final precoded signal is then given by x = v_{RF}v_{D}s.

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  • \$\begingroup\$ Context: copy and paste some text where these are mentioned. \$\endgroup\$ Commented Apr 19, 2020 at 9:44
  • \$\begingroup\$ Question edited. @Andyaka \$\endgroup\$ Commented Apr 19, 2020 at 10:10
  • \$\begingroup\$ What type of modulation is being used - can you describe the final (precoded) signal and carrier? Maybe you have a picture? \$\endgroup\$ Commented Apr 19, 2020 at 10:14
  • \$\begingroup\$ @Andyaka I haven't read it through...I just randomly opened a file and searched for the two words. And honestly, the question in your comment is a lot more difficult than what I am asking...if I knew the answer to your comment I probably wouldn't need to ask the question in the first place. I included a link to the paper in the question, if you are interested. \$\endgroup\$ Commented Apr 19, 2020 at 10:21

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A signal is a sequence of symbols transmitted sequentially over time.

A symbol is any distinct state of the communication channel.

For example, in a binary (two-state) channel, the states could be two voltage levels, two different values of current, or even two different frequencies — i.e., a simple modem. Such a channel can transmit one bit of information at a time.

Many types of channels can have more than two states, and this gives you the ability to transmit more than one bit at a time. For example, a 64-state channel can transmit 6 bits at a time, because 64 = 26. We say that each symbol represents 6 bits, and the channel capacity is the symbol rate (also sometimes called baud rate) multiplied by the number of bits per symbol.

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I do not have any references, but from my experience and understanding, a symbol is an information entity of a signal and a signal is the time-series of its information-associated symbols.

E.g. you can have a digital signal of a communication system with symbol levels -1V, +3V and +10V. So each symbol has ternary values and the time-series of the symbols is the communication signal.

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