In addition to providing channel information such as the rms delay spread, the power-delay profile фе(т), also provides a means for modeling the channel using a tapped-delay line (FIR) model. From Eq. (5), an(t) is the amplitude/gain coefficient for a path arriving with delay Tn(t). A typical power-de — lay profile is shown in Fig. 14, which in the second figure, is uniformly sampled into equal delay bins. In general, the different bins contain a number of received signals (corresponding to different paths) whose times of arrival lie within the particular delay bin. These signals are represented by an impulse at the center of each delay bin that has an amplitude with the appropriate statistical distribution (Rayleigh, Ri — cean, etc.). In deriving this model, two assumptions are made:

Time flat Frequency selective |
Time selective Frequency selective |

Frequency flat |
Time selective |

Time flat |
Frequency flat |

T> с я |

ї? со |

T 1 c |

B |

c |

Symbol duration (Ts)

Figure 13. A typical power delay profile and the method of sampling the power delay profile to generate a tapped-delay line model.

• there are sufficient number of rays clustered together in each delay bin;

• the statistical distribution of the envelope is known.

The rate of sampling the power-delay profile is affected by the time resolution desired and also the bandwidth of the transmitted signal. The next step after sampling the power-delay profile is to use a threshold (say X dB below the peak of the power-delay profile), and using the threshold to truncate

those samples below the threshold. This model can be implemented by using a tapped-delay line or FIK model, thereby allowing us to model any arbitrary channel.