## Unipolar vs bipolar symbols |
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.