# doppler.bell

Construct bell-shaped Doppler spectrum object

## Syntax

`doppler.bell`

doppler.bell(coeffbell)

## Description

doppler.bell creates a bell Doppler spectrum object. You can
use this object with the `DopplerSpectrum`

property
of any channel object created with either the `rayleighchan`

function,
the `ricianchan`

function, or `comm.MIMOChannel`

System object™.

dop = `doppler.bell`

creates a bell Doppler
spectrum object with default coefficient.

dop = `doppler.bell(coeffbell)`

creates a
bell Doppler spectrum object with coefficient given by `coeffbell`

,
where `coeffbell`

is a positive, finite, real scalar.

## Properties

The bell Doppler spectrum object has the following properties.

Property | Description |

SpectrumType | Fixed value, 'Bell' |

CoeffBell | Bell spectrum coefficient, positive real finite scalar. |

## Theory and Applications

A bell spectrum was proposed in [1] for the Doppler spectrum
of indoor MIMO channels, for 802.11n channel modeling.

The normalized bell Doppler spectrum is given analytically by:

$$S(f)=\frac{{C}_{b}}{1\text{}+\text{}A\text{\hspace{0.17em}}\text{}{\left(\frac{f}{{f}_{d}}\right)}^{2}}$$

where

$$\left|f\right|\le {f}_{d}$$

and

$${C}_{b}=\frac{\sqrt{A}}{\pi {f}_{d}}$$

*f*_{d} represents the
maximum Doppler shift specified for the channel object, and *A* represents
a positive real finite scalar (`CoeffBell`

). The
indoor MIMO channel model of IEEE 802.11n [1] uses the following parameter: *A* =
9. Since the channel is modeled as Rician fading with a fixed line-of-sight
(LOS) component, a Dirac delta is also present in the Doppler spectrum
at *f* = 0.

## Examples

Construct a bell Doppler spectrum object with a coefficient
of 8.5. Assign it to a Rayleigh channel object with one path.

dop = doppler.bell(8.5);
chan = rayleighchan(1e-5, 10);
chan.DopplerSpectrum = dop;

## References

[1] IEEE P802.11 Wireless LANs, "TGn Channel Models",
IEEE 802.1103/940r4, 2004-05-10.

#### Introduced in R2009a