Unipolar vs bipolar symbols

In Depth
In-depth

The energy per symbol for the unipolar waveform considered thus far is different depending on whether a logic 0 or logic 1 is sent, having a zero value for the logic 0 case. Assuming an equal likelihood of 1s and 0s being transmitted, the average energy per symbol sent is Es/2 where Es, as before, is the energy of the logic 1 symbol.

The symbol error probability for a unipolar binary data system with matched filtering is thus:

Ps  unipolar = 0.5·erfc(0.5·Es average/N0)1/2

If we now look at the bipolar data waveform where a logic 1 is conveyed as +V volts and a logic 0 as -V volts, we can show (see in-depth) that:

The symbol error probability for a bipolar waveform is given by:

Ps  bipolar = 0.5·erfc(Es average/N0)1/2


It is immediately apparent that the bipolar signalling method requires only half the average symbol energy for a given probability of error compared with the unipolar case.