**Subject :**Wireless Communication

## Impulse Response Model of a Multipath Channel

**Introduction: **

The impulse response Show the wideband channel characterization and it contains all information

used to simulate or analyze any type of radio transmission through the given channel.

The impulse response is a useful characterization of the channel, since it may be used to predict and compare the performance of many different mobile communication systems and transmission bandwidths for a particular mobile channel condition.

**impulse response**

- Consider the case where time variation is due strictly to receiver motion in space.The receiver moves along the ground at some constant velocity v. For a fixed position d, the channel between the transmitter and the receiver can be modeled as a linear time invariant system.(See figure given above)
- The channel impulse response can be expressed as h(d,t). Let x(t) represent the transmitted signal, then the received signal y(d,t) at position d can be expressed as a convolution of x (t) with h(d,t).

- For a causal system, h(d, t) = 0 for t< 0, thus equation reducesto

- Since the receiver moves along the ground at a constant velocity v, the position of the receiver can by expressed as

- Substituting value d in the equation, we obtain

- Since v is a constant, y(vt, t) is just a function of t. Therefore, equation can be expressed as

- From equation above it is clear that the mobile radio channel can be modeled as a linear time varying channel, where the channel changes with time and distance.h(t, τ) the impulse response of the time varying multipath radio channel.
- The variable t represents the time variations due to motion, whereas τ represents the channel multipath delay for a fixed value of t .
- The received signal y(t) can be expressed as a convolution of the transmitted signal x(t) with the channel impulse response is given as