# doppler.flat

Construct flat Doppler spectrum object

## Syntax

`dop = doppler.flat`

## Description

`dop = doppler.flat` creates a flat Doppler spectrum object that is to be used for the `DopplerSpectrum` property of a channel object (created with either the `rayleighchan` or the `ricianchan` function). The maximum Doppler shift of the flat Doppler spectrum object is specified by the `MaxDopplerShift` property of the channel object.

## Properties

The flat Doppler spectrum object contains only one property, `SpectrumType`, which is read-only and has a fixed value of `'Flat'`.

## Theory and Applications

In a 3-D isotropic scattering environment, where the angles of arrival are uniformly distributed in the azimuth and elevation planes, the Doppler spectrum is found theoretically to be flat [2]. A flat Doppler spectrum is also specified in some cases of the ANSI J-STD-008 reference channel models for PCS, for both outdoor (pedestrian) and indoor (commercial) [1] applications.

The normalized flat Doppler power spectrum is given analytically by:

where ${f}_{d}$ is the maximum Doppler frequency.

## Examples

collapse all

### Create a Rayleigh Channel with Flat Doppler Spectrum

This example shows how to create a Rayleigh channel object with a flat Doppler spectrum.

Set the sample time and maximum Doppler shift.

```ts = 1e-6; % sec fd = 50; % Hz ```

Create the Rayleigh channel object.

```chan = rayleighchan(ts,fd); ```

Observe that the default Doppler spectrum property, `SpectrumType`, is `'Jakes'` .

```chan.DopplerSpectrum ```
``` ans = SpectrumType: 'Jakes' ```

Change the Doppler spectrum property of the channel by using `doppler.flat`.

```chan.DopplerSpectrum = doppler.flat ```
``` chan = ChannelType: 'Rayleigh' InputSamplePeriod: 1.0000e-06 DopplerSpectrum: [1x1 doppler.flat] MaxDopplerShift: 50 PathDelays: 0 AvgPathGaindB: 0 NormalizePathGains: 1 StoreHistory: 0 StorePathGains: 0 PathGains: -0.6760 + 0.6319i ChannelFilterDelay: 0 ResetBeforeFiltering: 1 NumSamplesProcessed: 0 ```

## References

[1] ANSI J-STD-008, Personal Station-Base Station Compatibility Requirements for 1.8 to 2.0 GHz Code Division Multiple Access (CDMA) Personal Communications Systems, March 1995.

[2] Clarke, R. H., and Khoo, W. L., "3-D Mobile Radio Channel Statistics", IEEE Trans. Veh. Technol., Vol. 46, No. 3, pp. 798–799, August 1997.