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# Generic BCS Signals

Fundamentals | |
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Title | Generic BCS Signals |

Author(s) | J.A Ávila Rodríguez, University FAF Munich, Germany. |

Level | Advanced |

Year of Publication | 2011 |

Two particular cases of the BCS modulation are the BPSK and BOC modulations. Nonetheless, we show in the next lines how the Power Spectral Density (PSD) of a generic BCS could be derived.

Let us assume a BCS signal with vector s = [+1, +1, -1]. We have thus [math]\displaystyle{ s_1 = +1 , s_2 = +1 , s_3 = -1 }[/math]. The modulating term of the PSD can be easily calculated as:

which can be further simplified to:

while

Thus the spectrum of this BCS sequence would adopt the following form:

In general, in order to understand how the spectrum will look like for a given sequence, we have to be able to understand how every term of the sum above contributes to the total PSD.

## Credits

The information presented in this NAVIPEDIA’s article is an extract of the PhD work performed by Dr. Jose Ángel Ávila Rodríguez in the FAF University of Munich as part of his Doctoral Thesis “On Generalized Signal Waveforms for Satellite Navigation” presented in June 2008, Munich (Germany)