# doppler.bell

Construct bell-shaped Doppler spectrum object

## Syntax

`doppler.belldoppler.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.

PropertyDescription
SpectrumTypeFixed value, 'Bell'
CoeffBellBell 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:

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

where

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

and

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

fd 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;```