# GMSK Modulator Baseband

Modulate using Gaussian minimum shift keying method

## Library

CPM, in Digital Baseband sublibrary of Modulation

## Description

The GMSK Modulator Baseband block modulates using the Gaussian minimum shift keying method. The output is a baseband representation of the modulated signal.

The BT product parameter represents bandwidth multiplied by time. This parameter is a nonnegative scalar. It is used to reduce the bandwidth at the expense of increased intersymbol interference. The Pulse length parameter measures the length of the Gaussian pulse shape, in symbol intervals. For an explanation of the pulse shape, see the work by Anderson, Aulin, and Sundberg among the references listed below. The frequency pulse shape is defined by the following equations.

`$\begin{array}{l}g\left(t\right)=\frac{1}{2T}\left\{Q\left[2\pi {B}_{b}\frac{t-\frac{T}{2}}{\sqrt{\mathrm{ln}\left(2\right)}}\right]-Q\left[2\pi {B}_{b}\frac{t+\frac{T}{2}}{\sqrt{\mathrm{ln}\left(2\right)}}\right]\right\}\\ Q\left(t\right)=\underset{t}{\overset{\infty }{\int }}\frac{1}{\sqrt{2\pi }}{e}^{-{\tau }^{2}/2}d\tau \end{array}$`

For this block, an input symbol of 1 causes a phase shift of π/2 radians.

The group delay is the number of samples between the start of a filter's response and its peak. The group delay that the block introduces is Pulse length/2 * Samples per symbol (using a reference of output sample periods). For GMSK, Pulse length denotes the truncated frequency pulse length in symbols. The net delay effect at the receiver (demodulator) is due to the Traceback depth parameter, which in most cases would be larger than the group delay.

### Integer-Valued Signals and Binary-Valued Signals

When you set the Input type parameter to `Integer`, then the block accepts values of 1 and -1.

When you set the Input type parameter to `Bit`, then the block accepts values of 0 and 1.

This block accepts a scalar-valued or column vector input signal. For a column vector input signal, the width of the output equals the product of the number of symbols and the value for the Samples per symbol parameter.

### Single-Rate Processing

In single-rate processing mode, the input and output signals have the same port sample time. The block implicitly implements the rate change by making a size change at the output when compared to the input. In this mode, the input to the block can be multiple symbols.

• When you set Input type to `Integer`, the input can be a column vector, the length of which is the number of input symbols.

• When you set Input type to `Bit`, the input width must be an integer multiple of 2.

The output width equals the product of the number of input symbols and the Samples per symbol parameter value.

### Multirate Processing

In multirate processing mode, the input and output signals have different port sample times. In this mode, the input to the block must be one symbol.

• When you set Input type to `Integer`, the input must be a scalar.

• When you set Input type to `Bit`, the input width must equal the number of bits per symbol.

The output sample time equals the symbol period divided by the Samples per symbol parameter value.

## Parameters

Input type

Indicates whether the input consists of bipolar or binary values.

BT product

The product of bandwidth and time.

The block uses this parameter to reduce bandwidth at the expense of increased intersymbol interference. Enter a nonnegative scalar value for this parameter.

Pulse length (symbol intervals)

The length of the frequency pulse shape.

Symbol prehistory

A scalar or vector value that specifies the data symbols the block uses before the start of the simulation, in reverse chronological order. If it is a vector, then its length must be one less than the Pulse length parameter.

The initial phase of the output waveform, measured in radians.

Samples per symbol

The number of output samples that the block produces for each integer or bit in the input, which must be a positive integer. For all non-binary schemes, as defined by the pulse shapes, this value must be greater than 1.

For more information, see Upsample Signals and Rate Changes in Communications Toolbox™User's Guide.

Rate options

Select the rate processing option for the block.

• `Enforce single-rate processing` — When you select this option, the input and output signals have the same port sample time. The block implements the rate change by making a size change at the output when compared to the input. The output width equals the product of the number of symbols and the Samples per symbol parameter value.

• `Allow multirate processing` — When you select this option, the input and output signals have different port sample times. The output sample time equals the symbol period divided by the Samples per symbol parameter value.

Output data type

The output type of the block can be specified as a `single` or `double`. By default, the block sets this to `double`.

## Supported Data Types

PortSupported Data Types

Input

• Double-precision floating point

• Boolean (When Input type set to `Bit`)

• 8-, 16-, and 32-bit signed integers (When Input type set to `Integer`)

Output

• Double-precision floating point

• Single-precision floating point

## Pair Block

GMSK Demodulator Baseband

## References

[1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase Modulation. New York: Plenum Press, 1986.